Begge lærere siger, at der ofte kommer færre fejl, når man læser teksten langsomt.

Begge means both and can directly modify a plural noun:

• begge lærere = both teachers

Både is usually used in the pattern både ... og ...:

• både læreren og eleven = both the teacher and the student

So in this sentence, begge is the natural choice because it refers to two teachers as one plural group.

Lærere is the indefinite plural form: teachers.
Lærerne is the definite plural form: the teachers.

So:

• begge lærere = both teachers
• begge lærerne = both of the teachers / both the teachers

In many cases, Danish uses begge + indefinite plural noun where English might still naturally say both teachers.

Siger is the present tense form of at sige = to say.

• at sige = to say
• siger = say / says

Since the subject is begge lærere and the sentence is stating what they say in general, Danish uses the present tense:

• Begge lærere siger ... = Both teachers say ...

Unlike English, Danish present-tense verbs do not change depending on whether the subject is singular or plural.

Danish normally uses commas to mark subordinate clauses more clearly than English does. Here, at der ofte kommer færre fejl is a subordinate clause after siger.

So the comma separates:

• main clause: Begge lærere siger
• subordinate clause: at der ofte kommer færre fejl ...

In English, a comma before that is often omitted, but in Danish comma use is more systematic.

Here at means that and introduces a subordinate clause:

• siger, at ... = say that ...

Do not confuse this at with the infinitive marker to in phrases like at læse = to read. Danish uses the same word for both functions, but the grammar is different.

Here der is not really there in the physical-location sense. It is a formal or introductory subject, similar to English there in:

• There are fewer mistakes
• There come fewer mistakes (more literal, but unnatural English)

So:

• der kommer færre fejl = there are fewer mistakes / fewer mistakes occur

This kind of der is very common in Danish when introducing the existence or occurrence of something.

Literally, kommer means comes, but in Danish it is often used more broadly for things that appear, occur, or happen.

So:

• der kommer fejl can mean mistakes occur
• der kommer færre fejl = fewer mistakes occur

This is idiomatic Danish. English would usually not say fewer mistakes come, but Danish can use komme this way very naturally.

Because fejl is a countable noun: one mistake, two mistakes, three mistakes.

So Danish uses:

• få = few
• færre = fewer

Compare:

• færre fejl = fewer mistakes
• mindre tid = less time

Use færre with countable nouns and mindre with uncountable nouns.

This is because the clause after at is a subordinate clause, and Danish word order changes in subordinate clauses.

In a main clause, adverbs like ofte often come after the verb:

• Der kommer ofte færre fejl (main clause)

But in a subordinate clause, the adverb usually comes before the finite verb:

• at der ofte kommer færre fejl

This is a very important Danish pattern:

• main clause: verb before sentence adverb
• subordinate clause: sentence adverb before verb

Here man means one, you, or people in general.

So:

• når man læser teksten langsomt = when you read the text slowly / when one reads the text slowly

This man is an impersonal subject, not specifically a man in the sense of a male person.

It is very common in Danish for general statements:

• Man lærer hurtigt = You learn quickly / One learns quickly

Because the two clauses have different structures.

In når man læser teksten langsomt, the subject is man, and there is no sentence adverb placed before the verb, so the normal subordinate-clause order is:

• når + subject + verb + ...

In at der ofte kommer færre fejl, the adverb ofte is inserted, and in subordinate clauses such adverbs come before the finite verb:

• at + subject + adverb + verb + ...

So both are following normal Danish subordinate-clause word order.

Teksten means the text. Danish usually marks definiteness by adding an ending to the noun:

• tekst = a text
• teksten = the text

You could say den tekst in some contexts, but that usually adds emphasis or points out a particular text:

• den tekst = that text / that particular text

Here, teksten is the normal, neutral way to say the text.

Because langsomt is being used as an adverb: slowly.

The adjective is:

• langsom = slow

When used adverbially, many Danish adjectives take -t:

• Han er langsom = He is slow
• Han læser langsomt = He reads slowly

So:

• læser teksten langsomt = reads the text slowly

Often yes, but there is an important detail. Danish når is commonly used for:

• repeated or general situations: when(ever)
• future situations: when

So here:

• når man læser teksten langsomt = when you read the text slowly

This sounds like a general truth or repeated situation. If Danish wanted to refer to a single past event, da might be used instead in other contexts.

It breaks down like this:

• Begge lærere siger
  main clause: Both teachers say

• at der ofte kommer færre fejl
  subordinate clause after say: that there are often fewer mistakes

• når man læser teksten langsomt
  subordinate clause of time/condition: when you read the text slowly

So the sentence contains:

1. one main clause
2. a subordinate at-clause
3. a subordinate når-clause inside that larger statement

This is why the sentence has several commas and why the word order is not the same as in a simple main clause.